**Section formula :**

We use the section formula to find the point which divides the line segment in a given ratio.

The point P which divides the line segment joining the two points A (x_{1}, y_{1}) and B (x_{2}, y_{2}) internally in the ratio l : m is

If P divides a line segment AB joining the two points A (x_{1}, y_{1}) and B (x_{2}, y_{2}) externally in the ratio l : m is,

Let us look into some example problems based on the above concepts.

**Example 1 :**

Find the point which divide the line segment joining the points (-1,2) and (4,-5) internally in the ratio 2 : 3.

**Solution :**

Since we need to find the point which divides the line segment internally in the ratio 2 : 3, we have to use the formula

= (lx_{2} + mx_{1}) / (l + m), (ly_{2} + my_{1}) / (l + m)

Here (x_{1}, y_{1}) ==> (-1, 2) (x_{2}, y_{2}) ==> (4, -5) and l : m ==> 2:3

= 2(4) + 3(-1) / (2 + 3) , 2(-5) + 3(2) / (2 + 3)

= [(8 - 3) / 5 , (-10 + 6) / 5]

= (5 / 5 , -4 / 5)

= (1, -4/5)

Hence the point (1, -4/5) divides the line segment internally in the ratio 2 : 3.

**Example 2 :**

Find the point which divide the line segment joining the points (2, 1) and (3, 5) externally in the ratio 2 : 3.

**Solution :**

Since we need to find the point which divides the line segment externally in the ratio 2 : 3, we have to use the formula

= (lx_{2} - mx_{1}) / (l - m), (ly_{2} - my_{1}) / (l - m)

Here (x_{1}, y_{1}) ==> (2, 1) (x_{2}, y_{2}) ==> (3, 5) and l : m ==> 2:3

= 2(3) - 3(2) / (2 - 3) , 2(5) - 3(1) / (2 - 3)

= [(6 - 6) / 5 , (10 - 3) / 5]

= (0 / 5 , 7 / 5)

= (0, 7/5)

Hence the point (0, 7/5) divides the line segment externally in the ratio 2 : 3.

**Example 3 :**

Find the ratio in which x axis divides the line segment joining the points (6 , 4) and (1 ,- 7).

**Solution :**

Let l : m be the ratio of the line segment joining the points (6,4) and (1,-7) and let p(x,0) be the point on the x axis

Section formula internally

= (lx₂ + mx₁)/(l + m) , (ly₂ + my₁)/(l + m)

(x, 0) = [(1) + m(6)]/(l + m) , [l(-7) + m(4)]/(l + m)

(x , 0) = [l + 6 m]/(l + m) , [-7l + 4m]/(l + m)

Equating y-coordinates

[-7l + 4m]/(l + m) = 0

- 7 l + 4 m = 0

- 7 l = - 4 m

l/m = 4/7

l : m = 4 : 7

Hence x-axis divides the line segment in the ratio 4 : 7.

After having gone through the stuff given above, we hope that the students would have understood "Section Formula ".

If you want to know more about the stuff "Section Formula" Please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**

**Sum of all three four digit numbers formed using 0, 1, 2, 3**

**Sum of all three four digit numbers formed using 1, 2, 5, 6**